Question

A parallelogram has sides with lengths of `12` and `8`. If the parallelogram's area is `64`, what is the length of its longest diagonal?

Answer 1

longest diagonal =12.00053677

Explanation:

If we split the parallelogram into using the smaller diagonal, the area would be 32 `cm^2`

using Area=`1/2 xxa xxb xxsin C`

`32=1/2xx8xx12xxsin theta`

`sin theta=32/48=2/3`

`theta=sin^(-1) [2/3]`

`theta=41.8^@`

Therefore the other angle is `180-41.8=138.2^@`

Using the cosine rule to find the longest diagonal

`a^2=b^2+c^2-sxxbxxcxxcosA`

`a^2=12^2+8^2-12xx8xxsin 138.2^@`

`a^2=208-96sin138.2^@`

`a^2=144.0128829`

a=12.00053677